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<li class="navelem"><a class="el" href="namespacehelib.html">helib</a></li><li class="navelem"><a class="el" href="classhelib_1_1_p_algebra.html">PAlgebra</a></li>  </ul>
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<a href="#pub-methods">Public Member Functions</a> &#124;
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<div class="title">helib::PAlgebra Class Reference</div>  </div>
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<p>The structure of (Z/mZ)* /(p)  
 <a href="classhelib_1_1_p_algebra.html#details">More...</a></p>

<p><code>#include &lt;<a class="el" href="_p_algebra_8h_source.html">PAlgebra.h</a>&gt;</code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:abd266cd5f06d96f8628eed8aaf6ee7b7"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#abd266cd5f06d96f8628eed8aaf6ee7b7">PAlgebra</a> (long mm, long pp=2, const std::vector&lt; long &gt; &amp;_gens=std::vector&lt; long &gt;(), const std::vector&lt; long &gt; &amp;_ords=std::vector&lt; long &gt;())</td></tr>
<tr class="separator:abd266cd5f06d96f8628eed8aaf6ee7b7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6e1077c7f6b83071d3bcdd7370ecbe1a"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a6e1077c7f6b83071d3bcdd7370ecbe1a">operator==</a> (const <a class="el" href="classhelib_1_1_p_algebra.html">PAlgebra</a> &amp;other) const</td></tr>
<tr class="separator:a6e1077c7f6b83071d3bcdd7370ecbe1a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a794076ed8df723e12de03a2cdeadcc29"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a794076ed8df723e12de03a2cdeadcc29">operator!=</a> (const <a class="el" href="classhelib_1_1_p_algebra.html">PAlgebra</a> &amp;other) const</td></tr>
<tr class="separator:a794076ed8df723e12de03a2cdeadcc29"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a87dae80314766ef1cf15402f040bcd0d"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a87dae80314766ef1cf15402f040bcd0d">printout</a> () const</td></tr>
<tr class="memdesc:a87dae80314766ef1cf15402f040bcd0d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Prints the structure in a readable form.  <a href="classhelib_1_1_p_algebra.html#a87dae80314766ef1cf15402f040bcd0d">More...</a><br /></td></tr>
<tr class="separator:a87dae80314766ef1cf15402f040bcd0d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a888fa6fa19f172c9f1a27a60a273696c"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a888fa6fa19f172c9f1a27a60a273696c">printAll</a> () const</td></tr>
<tr class="separator:a888fa6fa19f172c9f1a27a60a273696c"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6852047dd695a0b1ae1a5ea03c3b2c53"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a6852047dd695a0b1ae1a5ea03c3b2c53">getM</a> () const</td></tr>
<tr class="memdesc:a6852047dd695a0b1ae1a5ea03c3b2c53"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns m.  <a href="classhelib_1_1_p_algebra.html#a6852047dd695a0b1ae1a5ea03c3b2c53">More...</a><br /></td></tr>
<tr class="separator:a6852047dd695a0b1ae1a5ea03c3b2c53"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5563b7dc7f0559d779bf869fbe4b3a5f"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a5563b7dc7f0559d779bf869fbe4b3a5f">getP</a> () const</td></tr>
<tr class="memdesc:a5563b7dc7f0559d779bf869fbe4b3a5f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns p.  <a href="classhelib_1_1_p_algebra.html#a5563b7dc7f0559d779bf869fbe4b3a5f">More...</a><br /></td></tr>
<tr class="separator:a5563b7dc7f0559d779bf869fbe4b3a5f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4422e1911052282a6881fa97ae5061dd"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a4422e1911052282a6881fa97ae5061dd">getPhiM</a> () const</td></tr>
<tr class="memdesc:a4422e1911052282a6881fa97ae5061dd"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns phi(m)  <a href="classhelib_1_1_p_algebra.html#a4422e1911052282a6881fa97ae5061dd">More...</a><br /></td></tr>
<tr class="separator:a4422e1911052282a6881fa97ae5061dd"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abc2f07b5e26ca6c049785b1e138c57b8"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#abc2f07b5e26ca6c049785b1e138c57b8">getOrdP</a> () const</td></tr>
<tr class="memdesc:abc2f07b5e26ca6c049785b1e138c57b8"><td class="mdescLeft">&#160;</td><td class="mdescRight">The order of p in (Z/mZ)^*.  <a href="classhelib_1_1_p_algebra.html#abc2f07b5e26ca6c049785b1e138c57b8">More...</a><br /></td></tr>
<tr class="separator:abc2f07b5e26ca6c049785b1e138c57b8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afb8bd85921189335d6d6f2fe30011907"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#afb8bd85921189335d6d6f2fe30011907">getNFactors</a> () const</td></tr>
<tr class="memdesc:afb8bd85921189335d6d6f2fe30011907"><td class="mdescLeft">&#160;</td><td class="mdescRight">The number of distinct prime factors of m.  <a href="classhelib_1_1_p_algebra.html#afb8bd85921189335d6d6f2fe30011907">More...</a><br /></td></tr>
<tr class="separator:afb8bd85921189335d6d6f2fe30011907"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad094fa9125ca7f35bece1480dbb870cb"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#ad094fa9125ca7f35bece1480dbb870cb">getRadM</a> () const</td></tr>
<tr class="memdesc:ad094fa9125ca7f35bece1480dbb870cb"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="classhelib_1_1_p_algebra.html#ad094fa9125ca7f35bece1480dbb870cb" title="getRadM() = prod of distinct prime factors of m">getRadM()</a> = prod of distinct prime factors of m  <a href="classhelib_1_1_p_algebra.html#ad094fa9125ca7f35bece1480dbb870cb">More...</a><br /></td></tr>
<tr class="separator:ad094fa9125ca7f35bece1480dbb870cb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa2ccff097bb152c82012046e0e781b62"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#aa2ccff097bb152c82012046e0e781b62">getNormBnd</a> () const</td></tr>
<tr class="memdesc:aa2ccff097bb152c82012046e0e781b62"><td class="mdescLeft">&#160;</td><td class="mdescRight">max-norm-on-pwfl-basis &lt;= normBnd * max-norm-canon-embed  <a href="classhelib_1_1_p_algebra.html#aa2ccff097bb152c82012046e0e781b62">More...</a><br /></td></tr>
<tr class="separator:aa2ccff097bb152c82012046e0e781b62"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad3d8dd3e7f2bab8486357e0f1e0cc01e"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#ad3d8dd3e7f2bab8486357e0f1e0cc01e">getPolyNormBnd</a> () const</td></tr>
<tr class="memdesc:ad3d8dd3e7f2bab8486357e0f1e0cc01e"><td class="mdescLeft">&#160;</td><td class="mdescRight">max-norm-on-pwfl-basis &lt;= polyNormBnd * max-norm-canon-embed  <a href="classhelib_1_1_p_algebra.html#ad3d8dd3e7f2bab8486357e0f1e0cc01e">More...</a><br /></td></tr>
<tr class="separator:ad3d8dd3e7f2bab8486357e0f1e0cc01e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5a90fd828a817490c390947228ecf928"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a5a90fd828a817490c390947228ecf928">getNSlots</a> () const</td></tr>
<tr class="memdesc:a5a90fd828a817490c390947228ecf928"><td class="mdescLeft">&#160;</td><td class="mdescRight">The number of plaintext slots = phi(m)/ord(p)  <a href="classhelib_1_1_p_algebra.html#a5a90fd828a817490c390947228ecf928">More...</a><br /></td></tr>
<tr class="separator:a5a90fd828a817490c390947228ecf928"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afd431a1ba58a00ffa22fa05a0b02da67"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#afd431a1ba58a00ffa22fa05a0b02da67">getPow2</a> () const</td></tr>
<tr class="memdesc:afd431a1ba58a00ffa22fa05a0b02da67"><td class="mdescLeft">&#160;</td><td class="mdescRight">if m = 2^k, then pow2 == k; otherwise, pow2 == 0  <a href="classhelib_1_1_p_algebra.html#afd431a1ba58a00ffa22fa05a0b02da67">More...</a><br /></td></tr>
<tr class="separator:afd431a1ba58a00ffa22fa05a0b02da67"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa5cacf4d0667eb9a921ba5b557a09632"><td class="memItemLeft" align="right" valign="top">const NTL::ZZX &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#aa5cacf4d0667eb9a921ba5b557a09632">getPhimX</a> () const</td></tr>
<tr class="memdesc:aa5cacf4d0667eb9a921ba5b557a09632"><td class="mdescLeft">&#160;</td><td class="mdescRight">The cyclotomix polynomial Phi_m(X)  <a href="classhelib_1_1_p_algebra.html#aa5cacf4d0667eb9a921ba5b557a09632">More...</a><br /></td></tr>
<tr class="separator:aa5cacf4d0667eb9a921ba5b557a09632"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a29eea1b1f91c49000f1ce02b5546e73a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a29eea1b1f91c49000f1ce02b5546e73a">set_cM</a> (double c)</td></tr>
<tr class="memdesc:a29eea1b1f91c49000f1ce02b5546e73a"><td class="mdescLeft">&#160;</td><td class="mdescRight">The "ring constant" cM.  <a href="classhelib_1_1_p_algebra.html#a29eea1b1f91c49000f1ce02b5546e73a">More...</a><br /></td></tr>
<tr class="separator:a29eea1b1f91c49000f1ce02b5546e73a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3dcfa1c03e7f17674c16e9d25687f87a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a3dcfa1c03e7f17674c16e9d25687f87a">get_cM</a> () const</td></tr>
<tr class="separator:a3dcfa1c03e7f17674c16e9d25687f87a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5e4b044f71ca8edcfa4426cb199461f0"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a5e4b044f71ca8edcfa4426cb199461f0">numOfGens</a> () const</td></tr>
<tr class="memdesc:a5e4b044f71ca8edcfa4426cb199461f0"><td class="mdescLeft">&#160;</td><td class="mdescRight">The prime-power factorization of m.  <a href="classhelib_1_1_p_algebra.html#a5e4b044f71ca8edcfa4426cb199461f0">More...</a><br /></td></tr>
<tr class="separator:a5e4b044f71ca8edcfa4426cb199461f0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa0f6448b824d27233d9fbed310a70641"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#aa0f6448b824d27233d9fbed310a70641">ZmStarGen</a> (long i) const</td></tr>
<tr class="memdesc:aa0f6448b824d27233d9fbed310a70641"><td class="mdescLeft">&#160;</td><td class="mdescRight">the i'th generator in (Z/mZ)^* /(p) (if any)  <a href="classhelib_1_1_p_algebra.html#aa0f6448b824d27233d9fbed310a70641">More...</a><br /></td></tr>
<tr class="separator:aa0f6448b824d27233d9fbed310a70641"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1e1a00b24fd8cef132e213b1b0c290bc"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a1e1a00b24fd8cef132e213b1b0c290bc">genToPow</a> (long i, long j) const</td></tr>
<tr class="memdesc:a1e1a00b24fd8cef132e213b1b0c290bc"><td class="mdescLeft">&#160;</td><td class="mdescRight">the i'th generator to the power j mod m  <a href="classhelib_1_1_p_algebra.html#a1e1a00b24fd8cef132e213b1b0c290bc">More...</a><br /></td></tr>
<tr class="separator:a1e1a00b24fd8cef132e213b1b0c290bc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6a60cd957fcf220607acafd96de3737d"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a6a60cd957fcf220607acafd96de3737d">frobeniusPow</a> (long j) const</td></tr>
<tr class="separator:a6a60cd957fcf220607acafd96de3737d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab01ff1a6b2a0eceba09d688a933de360"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#ab01ff1a6b2a0eceba09d688a933de360">OrderOf</a> (long i) const</td></tr>
<tr class="memdesc:ab01ff1a6b2a0eceba09d688a933de360"><td class="mdescLeft">&#160;</td><td class="mdescRight">The order of i'th generator (if any)  <a href="classhelib_1_1_p_algebra.html#ab01ff1a6b2a0eceba09d688a933de360">More...</a><br /></td></tr>
<tr class="separator:ab01ff1a6b2a0eceba09d688a933de360"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0388643441be4063002c63398b770361"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a0388643441be4063002c63398b770361">ProdOrdsFrom</a> (long i) const</td></tr>
<tr class="memdesc:a0388643441be4063002c63398b770361"><td class="mdescLeft">&#160;</td><td class="mdescRight">The product prod_{j=i}^{n-1} OrderOf(i)  <a href="classhelib_1_1_p_algebra.html#a0388643441be4063002c63398b770361">More...</a><br /></td></tr>
<tr class="separator:a0388643441be4063002c63398b770361"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a427d4228e407fbf694191ad18842e90d"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a427d4228e407fbf694191ad18842e90d">SameOrd</a> (long i) const</td></tr>
<tr class="memdesc:a427d4228e407fbf694191ad18842e90d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Is ord(i'th generator) the same as its order in (Z/mZ)^*?  <a href="classhelib_1_1_p_algebra.html#a427d4228e407fbf694191ad18842e90d">More...</a><br /></td></tr>
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<tr class="memitem:a6348a15c7c781dd026993577bf43a6cb"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a6348a15c7c781dd026993577bf43a6cb">FrobPerturb</a> (long i) const</td></tr>
<tr class="separator:a6348a15c7c781dd026993577bf43a6cb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr><td colspan="2"><div class="groupHeader">Translation between index, representatives, and exponents</div></td></tr>
<tr class="memitem:a09f3f7d864c1989663a51f43984777f3"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a09f3f7d864c1989663a51f43984777f3">ith_rep</a> (long i) const</td></tr>
<tr class="memdesc:a09f3f7d864c1989663a51f43984777f3"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the i'th element in T.  <a href="classhelib_1_1_p_algebra.html#a09f3f7d864c1989663a51f43984777f3">More...</a><br /></td></tr>
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<tr class="memitem:a8b99ace4bf35e1ff128147ca5d58e4d9"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a8b99ace4bf35e1ff128147ca5d58e4d9">indexOfRep</a> (long t) const</td></tr>
<tr class="memdesc:a8b99ace4bf35e1ff128147ca5d58e4d9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the index of t in T.  <a href="classhelib_1_1_p_algebra.html#a8b99ace4bf35e1ff128147ca5d58e4d9">More...</a><br /></td></tr>
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<tr class="memitem:a0bea13d33d64fcaab59ed2b0b5c5100a"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a0bea13d33d64fcaab59ed2b0b5c5100a">isRep</a> (long t) const</td></tr>
<tr class="memdesc:a0bea13d33d64fcaab59ed2b0b5c5100a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Is t in T?  <a href="classhelib_1_1_p_algebra.html#a0bea13d33d64fcaab59ed2b0b5c5100a">More...</a><br /></td></tr>
<tr class="separator:a0bea13d33d64fcaab59ed2b0b5c5100a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a99dfe4797026a43ffa9d5513b77eb709"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a99dfe4797026a43ffa9d5513b77eb709">indexInZmstar</a> (long t) const</td></tr>
<tr class="memdesc:a99dfe4797026a43ffa9d5513b77eb709"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the index of t in (Z/mZ)*.  <a href="classhelib_1_1_p_algebra.html#a99dfe4797026a43ffa9d5513b77eb709">More...</a><br /></td></tr>
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<tr class="memitem:ade7911f93f80ebe11cf7ba7a59fa921f"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#ade7911f93f80ebe11cf7ba7a59fa921f">indexInZmstar_unchecked</a> (long t) const</td></tr>
<tr class="memdesc:ade7911f93f80ebe11cf7ba7a59fa921f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns the index of t in (Z/mZ)* &ndash; no range checking.  <a href="classhelib_1_1_p_algebra.html#ade7911f93f80ebe11cf7ba7a59fa921f">More...</a><br /></td></tr>
<tr class="separator:ade7911f93f80ebe11cf7ba7a59fa921f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab3249eb57b3278851dafe777ddad1e29"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#ab3249eb57b3278851dafe777ddad1e29">repInZmstar_unchecked</a> (long idx) const</td></tr>
<tr class="memdesc:ab3249eb57b3278851dafe777ddad1e29"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns rep whose index is i.  <a href="classhelib_1_1_p_algebra.html#ab3249eb57b3278851dafe777ddad1e29">More...</a><br /></td></tr>
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<tr class="memitem:a30408cf321051115b46bb75f9c9cc898"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a30408cf321051115b46bb75f9c9cc898">inZmStar</a> (long t) const</td></tr>
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<tr class="memitem:a1f95fe47b88f5c8768a53f0b190d15bf"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a1f95fe47b88f5c8768a53f0b190d15bf">exponentiate</a> (const std::vector&lt; long &gt; &amp;exps, bool onlySameOrd=false) const</td></tr>
<tr class="memdesc:a1f95fe47b88f5c8768a53f0b190d15bf"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns prod_i gi^{exps[i]} mod m. If onlySameOrd=true, use only generators that have the same order as in (Z/mZ)^*.  <a href="classhelib_1_1_p_algebra.html#a1f95fe47b88f5c8768a53f0b190d15bf">More...</a><br /></td></tr>
<tr class="separator:a1f95fe47b88f5c8768a53f0b190d15bf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afb2bad9633f98f52f81a7670c0d9bef4"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#afb2bad9633f98f52f81a7670c0d9bef4">coordinate</a> (long i, long k) const</td></tr>
<tr class="memdesc:afb2bad9633f98f52f81a7670c0d9bef4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns coordinate of index k along the i'th dimension.  <a href="classhelib_1_1_p_algebra.html#afb2bad9633f98f52f81a7670c0d9bef4">More...</a><br /></td></tr>
<tr class="separator:afb2bad9633f98f52f81a7670c0d9bef4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae946c16cfbf1d51ae5b2fdb87d08ed89"><td class="memItemLeft" align="right" valign="top">std::pair&lt; long, long &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#ae946c16cfbf1d51ae5b2fdb87d08ed89">breakIndexByDim</a> (long idx, long dim) const</td></tr>
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<tr class="memitem:a39c3e8cd2438e3215d8b4d24cfd1f235"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a39c3e8cd2438e3215d8b4d24cfd1f235">assembleIndexByDim</a> (std::pair&lt; long, long &gt; idx, long dim) const</td></tr>
<tr class="memdesc:a39c3e8cd2438e3215d8b4d24cfd1f235"><td class="mdescLeft">&#160;</td><td class="mdescRight">The inverse of breakIndexByDim.  <a href="classhelib_1_1_p_algebra.html#a39c3e8cd2438e3215d8b4d24cfd1f235">More...</a><br /></td></tr>
<tr class="separator:a39c3e8cd2438e3215d8b4d24cfd1f235"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:adfc198eb325759da0eb07e1edad86a2b"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#adfc198eb325759da0eb07e1edad86a2b">addCoord</a> (long i, long k, long offset) const</td></tr>
<tr class="memdesc:adfc198eb325759da0eb07e1edad86a2b"><td class="mdescLeft">&#160;</td><td class="mdescRight">adds offset to index k in the i'th dimension  <a href="classhelib_1_1_p_algebra.html#adfc198eb325759da0eb07e1edad86a2b">More...</a><br /></td></tr>
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<tr class="memitem:a9b134922f5863ccdaa130a491cad0070"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a9b134922f5863ccdaa130a491cad0070">nextExpVector</a> (std::vector&lt; long &gt; &amp;exps) const</td></tr>
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<tr class="memitem:ae7353f229e73916f05088c9387728483"><td class="memItemLeft" align="right" valign="top">long&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#ae7353f229e73916f05088c9387728483">fftSizeNeeded</a> () const</td></tr>
<tr class="memdesc:ae7353f229e73916f05088c9387728483"><td class="mdescLeft">&#160;</td><td class="mdescRight">The largest FFT we need to handle degree-m polynomials.  <a href="classhelib_1_1_p_algebra.html#ae7353f229e73916f05088c9387728483">More...</a><br /></td></tr>
<tr class="separator:ae7353f229e73916f05088c9387728483"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5152c047d2440c4b26cbfb535b405cb2"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classhelib_1_1_p_g_f_f_t.html">PGFFT</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a5152c047d2440c4b26cbfb535b405cb2">getFFTInfo</a> () const</td></tr>
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<tr class="memitem:a3c01f838fab8cee32bc74602df146c79"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="structhelib_1_1half___f_f_t.html">half_FFT</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#a3c01f838fab8cee32bc74602df146c79">getHalfFFTInfo</a> () const</td></tr>
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<tr class="memitem:ab9403a0bcbcf9bf40931408891e283f9"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="structhelib_1_1quarter___f_f_t.html">quarter_FFT</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classhelib_1_1_p_algebra.html#ab9403a0bcbcf9bf40931408891e283f9">getQuarterFFTInfo</a> () const</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>The structure of (Z/mZ)* /(p) </p>
<p>A <a class="el" href="classhelib_1_1_p_algebra.html" title="The structure of (Z/mZ)* /(p)">PAlgebra</a> object is determined by an integer m and a prime p, where p does not divide m. It holds information describing the structure of (Z/mZ)^*, which is isomorphic to the Galois group over A = Z[X]/Phi_m(X)).</p>
<p>We represent (Z/mZ)^* as (Z/mZ)^* = (p) x (g1,g2,...) x (h1,h2,...) where the group generated by g1,g2,... consists of the elements that have the same order in (Z/mZ)^* as in (Z/mZ)^* /(p,g_1,...,g_{i-1}), and h1,h2,... generate the remaining quotient group (Z/mZ)^* /(p,g1,g2,...).</p>
<p>We let T subset (Z/mZ)^* be a set of representatives for the quotient group (Z/mZ)^* /(p), defined as T={ prod_i gi^{ei} * prod_j hj^{ej} } where the ei's range over 0,1,...,ord(gi)-1 and the ej's range over 0,1,...ord(hj)-1 (these last orders are in (Z/mZ)^* /(p,g1,g2,...)).</p>
<p>Phi_m(X) is factored as Phi_m(X)= prod_{t in T} F_t(X) mod p, where the F_t's are irreducible modulo p. An arbitrary factor is chosen as F_1, then for each t in T we associate with the index t the factor F_t(X) = GCD(F_1(X^t), Phi_m(X)).</p>
<p>Note that fixing a representation of the field R=(Z/pZ)[X]/F_1(X) and letting z be a root of F_1 in R (which is a primitive m-th root of unity in R), we get that F_t is the minimal polynomial of z^{1/t}. </p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
<a id="abd266cd5f06d96f8628eed8aaf6ee7b7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#abd266cd5f06d96f8628eed8aaf6ee7b7">&#9670;&nbsp;</a></span>PAlgebra()</h2>

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          <td class="memname">helib::PAlgebra::PAlgebra </td>
          <td>(</td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>mm</em>, </td>
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          <td class="paramkey"></td>
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          <td class="paramname"><em>pp</em> = <code>2</code>, </td>
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          <td class="paramtype">const std::vector&lt; long &gt; &amp;&#160;</td>
          <td class="paramname"><em>_gens</em> = <code>std::vector&lt;long&gt;()</code>, </td>
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          <td class="paramkey"></td>
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          <td class="paramtype">const std::vector&lt; long &gt; &amp;&#160;</td>
          <td class="paramname"><em>_ords</em> = <code>std::vector&lt;long&gt;()</code>&#160;</td>
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          <td>)</td>
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<h2 class="groupheader">Member Function Documentation</h2>
<a id="adfc198eb325759da0eb07e1edad86a2b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#adfc198eb325759da0eb07e1edad86a2b">&#9670;&nbsp;</a></span>addCoord()</h2>

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          <td>(</td>
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          <td class="paramname"><em>i</em>, </td>
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          <td class="paramname"><em>k</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>offset</em>&#160;</td>
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          <td></td>
          <td>)</td>
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<p>adds offset to index k in the i'th dimension </p>

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<a id="a39c3e8cd2438e3215d8b4d24cfd1f235"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a39c3e8cd2438e3215d8b4d24cfd1f235">&#9670;&nbsp;</a></span>assembleIndexByDim()</h2>

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          <td>(</td>
          <td class="paramtype">std::pair&lt; long, long &gt;&#160;</td>
          <td class="paramname"><em>idx</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>dim</em>&#160;</td>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>The inverse of breakIndexByDim. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ae946c16cfbf1d51ae5b2fdb87d08ed89">&#9670;&nbsp;</a></span>breakIndexByDim()</h2>

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          <td>(</td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>idx</em>, </td>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>dim</em>&#160;</td>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Break an index into the hypercube to index of the dimension-dim subcube and index inside that subcube. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#afb2bad9633f98f52f81a7670c0d9bef4">&#9670;&nbsp;</a></span>coordinate()</h2>

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          <td>(</td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>i</em>, </td>
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          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>k</em>&#160;</td>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Returns coordinate of index k along the i'th dimension. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a1f95fe47b88f5c8768a53f0b190d15bf">&#9670;&nbsp;</a></span>exponentiate()</h2>

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          <td class="memname">long helib::PAlgebra::exponentiate </td>
          <td>(</td>
          <td class="paramtype">const std::vector&lt; long &gt; &amp;&#160;</td>
          <td class="paramname"><em>exps</em>, </td>
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          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>Returns prod_i gi^{exps[i]} mod m. If onlySameOrd=true, use only generators that have the same order as in (Z/mZ)^*. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ae7353f229e73916f05088c9387728483">&#9670;&nbsp;</a></span>fftSizeNeeded()</h2>

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          <td class="memname">long helib::PAlgebra::fftSizeNeeded </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>The largest FFT we need to handle degree-m polynomials. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a6a60cd957fcf220607acafd96de3737d">&#9670;&nbsp;</a></span>frobeniusPow()</h2>

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          <td class="memname">long helib::PAlgebra::frobeniusPow </td>
          <td>(</td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>j</em></td><td>)</td>
          <td> const</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a6348a15c7c781dd026993577bf43a6cb">&#9670;&nbsp;</a></span>FrobPerturb()</h2>

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          <td>(</td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>i</em></td><td>)</td>
          <td> const</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a1e1a00b24fd8cef132e213b1b0c290bc">&#9670;&nbsp;</a></span>genToPow()</h2>

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          <td class="memname">long helib::PAlgebra::genToPow </td>
          <td>(</td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>i</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">long&#160;</td>
          <td class="paramname"><em>j</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td> const</td>
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<p>the i'th generator to the power j mod m </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a3dcfa1c03e7f17674c16e9d25687f87a">&#9670;&nbsp;</a></span>get_cM()</h2>

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          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a5152c047d2440c4b26cbfb535b405cb2">&#9670;&nbsp;</a></span>getFFTInfo()</h2>

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          <td class="memname">const <a class="el" href="classhelib_1_1_p_g_f_f_t.html">PGFFT</a>&amp; helib::PAlgebra::getFFTInfo </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a3c01f838fab8cee32bc74602df146c79">&#9670;&nbsp;</a></span>getHalfFFTInfo()</h2>

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          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a6852047dd695a0b1ae1a5ea03c3b2c53">&#9670;&nbsp;</a></span>getM()</h2>

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          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>Returns m. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#afb8bd85921189335d6d6f2fe30011907">&#9670;&nbsp;</a></span>getNFactors()</h2>

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          <td> const</td>
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<p>The number of distinct prime factors of m. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#aa2ccff097bb152c82012046e0e781b62">&#9670;&nbsp;</a></span>getNormBnd()</h2>

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          <td> const</td>
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<p>max-norm-on-pwfl-basis &lt;= normBnd * max-norm-canon-embed </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a5a90fd828a817490c390947228ecf928">&#9670;&nbsp;</a></span>getNSlots()</h2>

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          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>The number of plaintext slots = phi(m)/ord(p) </p>

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<h2 class="memtitle"><span class="permalink"><a href="#abc2f07b5e26ca6c049785b1e138c57b8">&#9670;&nbsp;</a></span>getOrdP()</h2>

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<p>The order of p in (Z/mZ)^*. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a5563b7dc7f0559d779bf869fbe4b3a5f">&#9670;&nbsp;</a></span>getP()</h2>

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<p>Returns p. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a4422e1911052282a6881fa97ae5061dd">&#9670;&nbsp;</a></span>getPhiM()</h2>

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          <td> const</td>
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<p>Returns phi(m) </p>

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<h2 class="memtitle"><span class="permalink"><a href="#aa5cacf4d0667eb9a921ba5b557a09632">&#9670;&nbsp;</a></span>getPhimX()</h2>

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          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>The cyclotomix polynomial Phi_m(X) </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ad3d8dd3e7f2bab8486357e0f1e0cc01e">&#9670;&nbsp;</a></span>getPolyNormBnd()</h2>

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          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>max-norm-on-pwfl-basis &lt;= polyNormBnd * max-norm-canon-embed </p>

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<h2 class="memtitle"><span class="permalink"><a href="#afd431a1ba58a00ffa22fa05a0b02da67">&#9670;&nbsp;</a></span>getPow2()</h2>

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          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p>if m = 2^k, then pow2 == k; otherwise, pow2 == 0 </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ab9403a0bcbcf9bf40931408891e283f9">&#9670;&nbsp;</a></span>getQuarterFFTInfo()</h2>

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          <td class="memname">const <a class="el" href="structhelib_1_1quarter___f_f_t.html">quarter_FFT</a>&amp; helib::PAlgebra::getQuarterFFTInfo </td>
          <td>(</td>
          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<h2 class="memtitle"><span class="permalink"><a href="#ad094fa9125ca7f35bece1480dbb870cb">&#9670;&nbsp;</a></span>getRadM()</h2>

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          <td class="paramname"></td><td>)</td>
          <td> const</td>
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<p><a class="el" href="classhelib_1_1_p_algebra.html#ad094fa9125ca7f35bece1480dbb870cb" title="getRadM() = prod of distinct prime factors of m">getRadM()</a> = prod of distinct prime factors of m </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a99dfe4797026a43ffa9d5513b77eb709">&#9670;&nbsp;</a></span>indexInZmstar()</h2>

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<p>Returns the index of t in (Z/mZ)*. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ade7911f93f80ebe11cf7ba7a59fa921f">&#9670;&nbsp;</a></span>indexInZmstar_unchecked()</h2>

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          <td class="paramtype">long&#160;</td>
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<p>Returns the index of t in (Z/mZ)* &ndash; no range checking. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a8b99ace4bf35e1ff128147ca5d58e4d9">&#9670;&nbsp;</a></span>indexOfRep()</h2>

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          <td> const</td>
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<p>Returns the index of t in T. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a30408cf321051115b46bb75f9c9cc898">&#9670;&nbsp;</a></span>inZmStar()</h2>

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          <td> const</td>
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<h2 class="memtitle"><span class="permalink"><a href="#a0bea13d33d64fcaab59ed2b0b5c5100a">&#9670;&nbsp;</a></span>isRep()</h2>

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<p>Is t in T? </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a09f3f7d864c1989663a51f43984777f3">&#9670;&nbsp;</a></span>ith_rep()</h2>

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          <td class="paramname"><em>i</em></td><td>)</td>
          <td> const</td>
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<p>Returns the i'th element in T. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a9b134922f5863ccdaa130a491cad0070">&#9670;&nbsp;</a></span>nextExpVector()</h2>

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<p>exps is an array of exponents (the dLog of some t in T), this function increment exps lexicographic order, return false if it cannot be incremented (because it is at its maximum value) </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a5e4b044f71ca8edcfa4426cb199461f0">&#9670;&nbsp;</a></span>numOfGens()</h2>

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<p>The prime-power factorization of m. </p>
<p>The number of generators in (Z/mZ)^* /(p) </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a794076ed8df723e12de03a2cdeadcc29">&#9670;&nbsp;</a></span>operator!=()</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#ab01ff1a6b2a0eceba09d688a933de360">&#9670;&nbsp;</a></span>OrderOf()</h2>

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<p>The order of i'th generator (if any) </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a888fa6fa19f172c9f1a27a60a273696c">&#9670;&nbsp;</a></span>printAll()</h2>

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<h2 class="memtitle"><span class="permalink"><a href="#a87dae80314766ef1cf15402f040bcd0d">&#9670;&nbsp;</a></span>printout()</h2>

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<p>Prints the structure in a readable form. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a0388643441be4063002c63398b770361">&#9670;&nbsp;</a></span>ProdOrdsFrom()</h2>

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<p>The product prod_{j=i}^{n-1} OrderOf(i) </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ab3249eb57b3278851dafe777ddad1e29">&#9670;&nbsp;</a></span>repInZmstar_unchecked()</h2>

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<p>Returns rep whose index is i. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a427d4228e407fbf694191ad18842e90d">&#9670;&nbsp;</a></span>SameOrd()</h2>

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<p>Is ord(i'th generator) the same as its order in (Z/mZ)^*? </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a29eea1b1f91c49000f1ce02b5546e73a">&#9670;&nbsp;</a></span>set_cM()</h2>

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<p>The "ring constant" cM. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#aa0f6448b824d27233d9fbed310a70641">&#9670;&nbsp;</a></span>ZmStarGen()</h2>

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<p>the i'th generator in (Z/mZ)^* /(p) (if any) </p>

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<hr/>The documentation for this class was generated from the following files:<ul>
<li>/HElib/include/helib/<a class="el" href="_p_algebra_8h_source.html">PAlgebra.h</a></li>
<li>/HElib/src/<a class="el" href="_p_algebra_8cpp.html">PAlgebra.cpp</a></li>
</ul>
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